orientation

Algorithms that deal with orientation.

Functions

orient(k)	Orient an unoriented diagram using the default edge directions.
orient_edges(k, edge_paths)	Orient an unoriented diagram along given edge paths.
orientations(k[, up_to_reversal])	Generate all orientations of an unoriented diagram.
reverse(k[, inplace])	Reverse orientation of an oriented diagram.
unorient(k)	Return an unoriented copy of the diagram.

orient(k)

Orient an unoriented diagram using the default edge directions.

This picks the natural direction for every edge returned by knotpy.algorithms.topology.edges().

Parameters:

k (PlanarDiagram) – Unoriented diagram.

Returns:

Oriented diagram.

Return type:

OrientedPlanarDiagram

Example

>>> import knotpy as kp
>>> k = kp.knot("3_1")
>>> kp.orient(k)
Diagram named 3_1 a → X(b3o c0i c3i b0o), b → X(a3i c2o c1o a0i), c → X(a1o b2i b1i a2o)

unorient(k)

Return an unoriented copy of the diagram.

Parameters:

k (OrientedPlanarDiagram | PlanarDiagram)

Return type:

PlanarDiagram

orientations(k, up_to_reversal=False)

Generate all orientations of an unoriented diagram.

If up_to_reversal is True, the first edge is always oriented “forward” and only the remaining edges are flipped (removing a global reversal).

Parameters:

• k (PlanarDiagram) – Unoriented diagram.

• up_to_reversal (bool) – If True, return orientations modulo global reversal.

Returns:

List of OrientedPlanarDiagram.

Return type:

list[OrientedPlanarDiagram]

Notes

• If k is already oriented, it is first “unoriented” (structure preserved) and then all orientations are generated.

• If k.name is set, each result’s name is suffixed with a string of “+”/“–” per-edge choices (useful for debugging).

Example

>>> import knotpy as kp
>>> k = kp.knot("3_1")
>>> k1, k2 = kp.orientations(k)
>>> print(f'Oriented trefoils: {k1} and {k2}')
Oriented diagrams: Diagram named 3_1+ a → X(b3o c0i c3i b0o), b → X(a3i c2o c1o a0i), c → X(a1o b2i b1i a2o) and Diagram named 3_1- a → X(b3i c0o c3o b0i), b → X(a3o c2i c1i a0o), c → X(a1i b2o b1o a2i)

reverse(k, inplace=False)

Reverse orientation of an oriented diagram.

Swaps each arc’s endpoint types (ingoing/outgoing) accordingly.

Parameters:

• k (OrientedPlanarDiagram) – Oriented planar diagram to reverse.

• inplace (bool) – If True, modify k in place, otherwise return a copy.

Returns:

The orientation-reversed diagram.

Raises:

TypeError – If k is an unoriented PlanarDiagram.

Return type:

OrientedPlanarDiagram